Case studies and classroom examples from more than four decades of work with children, families and schools. Each one sets out what was done, what was observed and what it can and can't tell us.
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The Bamboo Mental Maths program was used in schools across Chile and Peru. Students completed an initial and a final assessment in each level. On average, the number of correct answers approximately doubled between the initial and final assessments. Individual results vary.
Addition & Subtraction
Level 12,800 students
Years 1 to 3
Addition & Subtraction
Level 21,829 students
Years 1 to 3
Addition & Subtraction
Level 31,535 students
Years 2 to 3
Multiplication
Level 12,091 students
Years 3 to 6
Multiplication
Level 21,248 students
Years 3 to 6
Multiplication
Level 31,369 students
Years 3 to 6
The assessments show improvements in mental maths performance over the program period. They do not, on their own, establish that the Langford Method caused the improvements or measure changes in the six habits. Classroom observations and educator experiences provide additional perspectives on how children work and participate.
What initial and final assessments revealed about progress among 10,872 students in Chile and Peru.
Read and download PDFAn early-childhood project exploring foundational abilities and participation in learning.
Read and download PDFHow teachers at Domingo Urrutia described changes in their practice and classroom learning conditions.
Read and download PDFHow school leadership and shared teaching practices supported a change in expectations and participation.
Read and download PDFHow a rural school organised learning for children from three year levels in one classroom.
Read and download PDFA 2015 assessment exploring students' accuracy and fluency in basic mental calculation across school year levels.
Read and download PDFAn investigation of foundational skills and classroom participation that helped shape Sylvia's focus on childhood.
Read and download PDFVocabulary learning with more than 3,500 adult English learners, and how this experience later shaped the Boomerang program.
Read and download PDFSylvia Langford's retrospective account of clinical work with 103 patients aged 2–25, exploring consistency, expectations and participation.
Read and download PDFFind out which habit may be a useful place to start.
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